Oscillatory Behavior of Three Dimensional <i>α</i>-Fractional Delay Differential Systems
In the present work we study the oscillatory behavior of three dimensional <inline-formula> <math display="inline"> <semantics> <mi>α</mi> </semantics> </math> </inline-formula>-fractional nonlinear delay differential system. We esta...
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| Format: | Article |
| Language: | English |
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MDPI AG
2018-12-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/10/12/769 |
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| author | Adem Kilicman Vadivel Sadhasivam Muthusamy Deepa Nagamanickam Nagajothi |
| author_facet | Adem Kilicman Vadivel Sadhasivam Muthusamy Deepa Nagamanickam Nagajothi |
| author_sort | Adem Kilicman |
| collection | DOAJ |
| description | In the present work we study the oscillatory behavior of three dimensional <inline-formula> <math display="inline"> <semantics> <mi>α</mi> </semantics> </math> </inline-formula>-fractional nonlinear delay differential system. We establish some sufficient conditions that will ensure all solutions are either oscillatory or converges to zero, by using the inequality technique and generalized Riccati transformation. The newly derived criterion are also used to establish a new class of systems with delay which are not covered in the existing study of literature. Further, we constructed some suitable illustrations. |
| first_indexed | 2024-04-11T21:48:39Z |
| format | Article |
| id | doaj.art-8177dba3cd73441790d258a22188cbf5 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-04-11T21:48:39Z |
| publishDate | 2018-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-8177dba3cd73441790d258a22188cbf52022-12-22T04:01:18ZengMDPI AGSymmetry2073-89942018-12-01101276910.3390/sym10120769sym10120769Oscillatory Behavior of Three Dimensional <i>α</i>-Fractional Delay Differential SystemsAdem Kilicman0Vadivel Sadhasivam1Muthusamy Deepa2Nagamanickam Nagajothi3Department of Mathematics and Institute for Mathematical Research, Universiti Putra Malaysia, Serdang 43400 UPM, Selangor, MalaysiaPost Graduate and Research Department of Mathematics, Thiruvalluvar Government Arts College (Periyar University), Rasipuram 637 401, Namakkal Dt., IndiaPost Graduate and Research Department of Mathematics, Thiruvalluvar Government Arts College (Periyar University), Rasipuram 637 401, Namakkal Dt., IndiaPost Graduate and Research Department of Mathematics, Thiruvalluvar Government Arts College (Periyar University), Rasipuram 637 401, Namakkal Dt., IndiaIn the present work we study the oscillatory behavior of three dimensional <inline-formula> <math display="inline"> <semantics> <mi>α</mi> </semantics> </math> </inline-formula>-fractional nonlinear delay differential system. We establish some sufficient conditions that will ensure all solutions are either oscillatory or converges to zero, by using the inequality technique and generalized Riccati transformation. The newly derived criterion are also used to establish a new class of systems with delay which are not covered in the existing study of literature. Further, we constructed some suitable illustrations.https://www.mdpi.com/2073-8994/10/12/769oscillationnonlinear differential systemdelay differential system<i>α</i>-fractional derivative |
| spellingShingle | Adem Kilicman Vadivel Sadhasivam Muthusamy Deepa Nagamanickam Nagajothi Oscillatory Behavior of Three Dimensional <i>α</i>-Fractional Delay Differential Systems Symmetry oscillation nonlinear differential system delay differential system <i>α</i>-fractional derivative |
| title | Oscillatory Behavior of Three Dimensional <i>α</i>-Fractional Delay Differential Systems |
| title_full | Oscillatory Behavior of Three Dimensional <i>α</i>-Fractional Delay Differential Systems |
| title_fullStr | Oscillatory Behavior of Three Dimensional <i>α</i>-Fractional Delay Differential Systems |
| title_full_unstemmed | Oscillatory Behavior of Three Dimensional <i>α</i>-Fractional Delay Differential Systems |
| title_short | Oscillatory Behavior of Three Dimensional <i>α</i>-Fractional Delay Differential Systems |
| title_sort | oscillatory behavior of three dimensional i α i fractional delay differential systems |
| topic | oscillation nonlinear differential system delay differential system <i>α</i>-fractional derivative |
| url | https://www.mdpi.com/2073-8994/10/12/769 |
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